Even though I'm a geologist by training, I do teach courses on Observational Astronomy and Ancient Astronomy (both offered this fall semester, the Observational Astronomy on Thursday nights and the Ancient Astronomy online - contact me if you're interested!).
Over the next few days, I'll be posting some information about the movements of the Moon and I'll start with the most obvious things and then move on to the more subtle movements. Let's start with the phases of the Moon.
Moon "phases" refer to the percentage and portion of the Moon illuminated by the Sun as seen from the Earth's surface. A New Moon is not illuminated and invisible. A Full Moon is 100% illuminated. The time it takes to go from the New Moon to the Full Moon and back to the New Moon is one cycle of phases and takes about a month (the words "moon" and "month" are obviously cognates).